CLEVELAND – Zach McAllister didn’t pitch poorly in his first big league appearance since May 21. He also didn’t pitch well enough to end his long victory drought.

All-Star first baseman Jose Abreu hit his major league-leading 29th home run, a two-run shot in the fourth inning, as the Chicago White Sox beat the Cleveland Indians 6-2 on Saturday.

Chicago only managed four hits against McAllister (3-5) in seven innings, but scored three times to keep him winless since April 21. The right-hander is 0-5 with an 8.22 ERA in his past seven starts, bridging a one-month stay on the disabled list with a sore back and a demotion to Triple-A Columbus.

“I was extremely happy with the way I pitched, but it obviously would have been a lot better if we had got the win,” said McAllister, who had a 5-0 record and 2.23 ERA with the Clippers.

“I felt like I got in a good groove, but made a couple of mistakes to Abreu and (Adam) Dunn. Those two big swings really hurt me but that also shows I was in a pretty good place because it was only one or two mistakes, not a lot of them.”

McAllister threw three perfect innings before allowing a leadoff walk to Alexei Ramirez in the fourth. Abreu hit the next pitch into the White Sox bullpen, and Dunn had an RBI double in the sixth to extend Chicago’s lead to 3-0.

“Zach came out real aggressive and was pretty effective today, which is what we wanted to see from him,” Cleveland manager Terry Francona said. “He left a breaking ball over to Abreu and Dunn also got a hold of one, but I thought he was OK.”

Jason Kipnis drew a bases-loaded walk against White Sox reliever Zach Putnam in the seventh. All-Star outfielder Michael Brantley hit a solo homer in the eighth against Eric Surkamp to pull the Indians within 3-2. It was Brantley’s career-high 15th home run and extended his hitting streak to nine games.

Francona allowed right-hander Austin Adams, called up from the minors Friday, to make his major league debut to start the ninth. He only recorded one out and allowed three runs.

“I didn’t want Austin to go to next week without pitching, but it kind of didn’t work very well,” Francona said.

White Sox right-hander Scott Carroll (4-5) pitched five scoreless frames before exiting with a stiff lower back. The rookie hasn’t allowed an earned run against the Indians in 14 innings, but has a 5.27 ERA against the rest of baseball.

“Carroll was keeping the ball down, doing a good job pitching the whole way,” Brantley said. “Zach did a real good job for us, too. But we didn’t do our part. As an offense, we’ve got to pick him up. That’s our responsibility.”

The Indians moved designated hitter Jason Giambi (sore left knee) to the 60-day disabled list after the game. Giambi, batting .128 with two homers and five RBI in 15 games, had been on the 15-day DL since June 12.

Before the game, Francona said Giambi “definitely” will play again this season. Giambi fractured a rib in spring training and began the season on the DL. He was activated April 21, but a strained call landed him on the DL again May 5.

The move was made after Cleveland acquired left-hander Nick Maronde in a minor league trade with the Angels and added him to the 40-man roster.

Notes

The Indians optioned RHP Vinnie Pestano to Triple-A Columbus in order to make room for McAllister on their 25-man roster. Pestano went 0-1 with a 5.00 ERA in 13 appearances. ... Indians OF Chris Dickerson (left hamstring tightness) was a late scratch from the lineup. Mike Aviles took his spot in left field, going 1 for 4. ... C Yan Gomes hit a line drive in the seventh that originally was called a catch but was overturned to a single after Francona challenged the ruling. Francona is 11 for 21 on replay challenges this season. ... Browns QB Brian Hoyer, a Cleveland native, threw out the ceremonial first pitch. ... Indians RHP Trevor Bauer (3-4) takes on White Sox LHP John Danks (8-6) in the three-game series finale today.